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How Alike Is It Versus How Likely Is It: A Disjunction Fallacy in Probability Judgments

Authors:

Maya Bar-Hillel & Efrat Neter

Abstract:

Formally, a conjunction fallacy and a disjunction fallacy cannot be distinguished. Both consist of a violation of the rule that an event cannot be more probable than another event which includes it. Hitherto, only a special kind of violation of this rule has been demonstrated, namely, that people sometimes judge the probability of A & B to be higher than the probability of A (Tversky & Kahneman, 1983). This study demonstrates a violation of the rule in a context that justifies the label disjunction fallacy. Subjects received brief case descriptions, and ordered seven categories according to one of four criteria for including the case as a member of the category : 1. probability of membership ; 2. willingness to bet on membership ; 3. inclination to predict membership ; 4. suitability for membership. The category list included nested pairs of categories, such as Brazil and South American country, or Physics and A Natural Science. The more inclusive category was a union of basic level sets like the smaller category. From a normative standpoint, the first two criteria are equivalent, and either ranking a category as more probable than its superordinate, or betting on it rather than on its superordinate, is fallacious. On the other hand, inclination to predict may be guided by the desire to be maximize informativeness rather than merely likelihood of being correct, and suitability needs to conform to no formal rule. Hence, with respect to these two criteria, such a ranking pattern is not fallacious. In spite of this crucial difference, subjects in all four groups rendered highly similar judgments, and the ranking of categories higher than their superodinates was not lower when it amounted to a fallacy than when it did not. The results support the representativeness thesis against some alternative interpretations.